Question

In a regular deck of cards calculate the probability that a face card is drawn given that it is a heart

Answer 1

So what are you asking? Or are you answering your own question

Answer 2

Answer:

Option 4) Probability = 30%            

Step-by-step explanation:

We are given the following information:

We have a deck of cards.

We have to find the probability of drawing a face card given that is a heart.

Formula:

$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$

Conditional probability:

The probability of happening of event A given event B:

$P(A|B) = \displaystyle\frac{P(A \cap B)}{P(B)}$

$P(\text{Face card}|\text{Hearts}) = \displaystyle\frac{P(\text{Face card} \cap \text{Hearts})}{P(\text{Hearts)}}\\P(\text{Hearts}) = \displaystyle\frac{13}{52}\\\\P(\text{Face card} \cap \text{Hearts}) = \frac{4}{52}\\\\P(\text{Face card}|\text{Hearts}) = \frac{4/52}{13/52} = \frac{4}{13}\\\\=\frac{4}{13}\times 100\% = 30.77\%$